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Determine the length of the given side for the congruent quadrilaterals ABCD and A'B'C'D'. The length of side A'B' The length of side A'B' is D A 9 B 133 0 65° 21 C 52° В' A' L 5

Determine the length of the given side for the congruent quadrilaterals ABCD and A'B'C'D'. The length of side A'B' The length of side A'B' is D A 9 B 133 0 65° 21 C 52° В' A' L 5

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Problem Statement Determine the length of the given side for the congruent quadrilaterals \(ABCD\) and \(A'B'C'D'\). The length of side \( \overline{A'B'} \) is _______. ### Diagrams 1. **Quadrilateral \(ABCD\)**: - Side \(AB = 9\) - Side \(BC = 21\) - Angle \(DAB = 65^\circ\) - Angle \(ABC = 133^\circ\) 2. **Quadrilateral \(A'B'C'D'\)**: - Side \(A'D' = 5\) - Angle \(C'D'A' = 52^\circ\) ### Solution Since quadrilaterals \(ABCD\) and \(A'B'C'D'\) are congruent, corresponding sides and angles are equal. Use the given information to determine the unknown length: - \( \overline{CD} \) corresponds to \( \overline{C'D'} \). - Given \( \overline{C'D'} = 5 \), the length of side \( \overline{A'B'} \) is equal to the corresponding side \( \overline{AB} = 9 \). Thus, the length of side \( \overline{A'B'} \) is \(\boxed{9}\).
Transcribed Image Text:### Problem Statement Determine the length of the given side for the congruent quadrilaterals \(ABCD\) and \(A'B'C'D'\). The length of side \( \overline{A'B'} \) is _______. ### Diagrams 1. **Quadrilateral \(ABCD\)**: - Side \(AB = 9\) - Side \(BC = 21\) - Angle \(DAB = 65^\circ\) - Angle \(ABC = 133^\circ\) 2. **Quadrilateral \(A'B'C'D'\)**: - Side \(A'D' = 5\) - Angle \(C'D'A' = 52^\circ\) ### Solution Since quadrilaterals \(ABCD\) and \(A'B'C'D'\) are congruent, corresponding sides and angles are equal. Use the given information to determine the unknown length: - \( \overline{CD} \) corresponds to \( \overline{C'D'} \). - Given \( \overline{C'D'} = 5 \), the length of side \( \overline{A'B'} \) is equal to the corresponding side \( \overline{AB} = 9 \). Thus, the length of side \( \overline{A'B'} \) is \(\boxed{9}\).
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